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%I #19 Oct 07 2017 02:59:00
%S 30,2176,54036,709956,6290051,42606671,237197942,1135834242,
%T 4823607212,18563958502,65783057592,217240417628,674884181813,
%U 1987124979703,5579019610088,15010371955248,38862554420034,97163223921924,235290234202584,553296290481584
%N Number of 5-element ordered antichain covers of an unlabeled n-element set.
%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H G. C. Greubel, <a href="/A056093/b056093.txt">Table of n, a(n) for n = 4..1000</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%F a(n)=C(n + 30, 30) - 20*C(n + 22, 22) + 60*C(n + 18, 18) + 20*C(n + 16, 16) + 10*C(n + 15, 15) - 110*C(n + 14, 14) - 120*C(n + 13, 13) + 150*C(n + 12, 12) + 120*C(n + 11, 11) - 240*C(n + 10, 10) + 20*C(n + 9, 9) + 240*C(n + 8, 8) + 40*C(n + 7, 7) - 205*C(n + 6, 6) + 60*C(n + 5, 5) - 210*C(n + 4, 4) + 210*C(n + 3, 3) + 50*C(n + 2, 2) - 100*C(n + 1, 1) + 24*C(n, 0).
%t Table[Binomial[n+30,30]-20 Binomial[n+22,22]+60 Binomial[n+18,18]+ 20 Binomial[n+16,16]+ 10 Binomial[n+15,15]-110 Binomial[n+14,14]- 120 Binomial[n+13,13]+ 150 Binomial[n+12,12]+ 120 Binomial[n+11,11]- 240 Binomial[n+10,10]+ 20 Binomial[n+9,9]+ 240 Binomial[n+8,8]+ 40 Binomial[n+7,7]- 205 Binomial[n+6,6]+ 60 Binomial[n+5,5]- 210 Binomial[n+4,4]+ 210 Binomial[n+3,3]+ 50 Binomial[n+2,2]- 100 Binomial[n+1,1]+ 24 Binomial[n,0],{n,4,30}] (* _Harvey P. Dale_, Sep 06 2011 *)
%Y Cf. A056048 for 5-antichain (unordered) covers of a labeled n-set, A051113. See also A056074, A056090.
%K nonn
%O 4,1
%A _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic, Jul 27 2000
%E More terms from _Harvey P. Dale_, Sep 06 2011
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